Step 1: Week 5 kickoff meeting – Monday 10:10 am
- Join us for the weekly live meeting and lecture via the link in Canvas
(or watch the recording later)
- Agenda: Logistics, note changed Thursday time for this week (oops, update: now it is changed back to the usual 4-6pm time!), lecture/discussion about the Fundamental Theorem of Calculus, why it is true, and how to use it to solve definite integrals.
Step 2: Get started on the WebAssign homework
- Log into WebAssign from Canvas and start the Section 7.5 homework
- Be sure to use the e-book when you need help and to look at relevant definitions, theorems, and examples
- All of the problems in this homework assignment are computations of definite integrals using the Fundamental Theorem of Calculus.
- Problems 1-2 and 4-6 are about using the Fundamental Theorem of Calculus to solve definite integrals involving relatively simple algebraic functions. Many of the integrands will need to be simplified or rewritten before antidifferentiation rules can be applied.
- For these problems, and all the problems in this section, you’ll be using Theorem 7.22 (the Fundamental Theorem of Calculus). For these first problems the antidifferentiation step uses Theorem 7.16(a) from the previous section.
- Example 2(a) shows a very basic example of solving the definite integral of a polynomial.
- This Khan Academy video on the Definite integral with the reverse power rule is a very basic introduction to using the Fundamental Theorem of Calculus simple power functions
- This Khan Academy video on the Definite integral of a radical function should help you if you get stuck on Problem 5.
- Problems 3 and 7 are about the same thing, but with exponential functions. Again, some preliminary algebra/rewriting may be useful.
- Example 3 shows how to apply the Fundamental Theorem of Calculus when simple exponential functions are involved. For this second block of problems the antidifferentiation step uses Theorem 7.17 from the previous section.
- The Taalman/Kohn Calc Clips video on Solving Definite Integrals with the Fundamental Theorem of Calculus is a little harder than these problems but is along the same lines.
- Problems 8-9 are about the same thing, but with trigonometric functions.
- Example 2(b) provides an easy starting point; often for these types of problems the hardest part is remembering how to evaluate the trigonometric functions after anti-differentiating.
- Theorem 7.18 from the previous section has the antidifferentiation formulas that you may need for these types of problems.
- This Khan Academy video on the Definite integral of a trigonometric function goes more in depth and has a more challenging evaluation step at the end.
- Problems 10-13 are where things start to get tricky; you may need to consider logarithmic functions, inverse trigonometric functions, and even guess-and-check techniques with the reverse chain rule. This is where what you learned in the previous section will come into play; if you get stuck, try reviewing the reading and recommended videos for Section 7.4.
- See Theorem 7.16(b) in the previous section for logarithmic antiderivatives.
- See Theorem 7.19(a) and (b) from the previous section for inverse trigonometric antiderivative formulas.
- See Theorem 7.21(c) from the previous section for the reverse chain rule formula.
- IMPORTANT NOTE – The Section 7.5 Mastery Quiz problems will be based on the problems above but not all of them will ask for numerical final answers. Some problems will ask you things about how you solved these problems and the techniques that apply to different types of problems.
Step 3: Take a break
- We keep on keeping on. Take a break, laugh at something, talk to somebody, pet your cat. Then get back to it. You can do this.
Step 4: Get help if you need it… and finish the homework
- *USUAL* TIME THIS WEEK AFTER ALL – Zoom drop-in 4-6pm Thursday (link in Canvas)
- Or, if you can’t attend, watch the recording (link to be added in Canvas later)
- Agenda: Discuss wekly updates, get math help, ask Dr. Taalman anything
- FUN EXTRA OPTIONAL EVENT – I’m giving a talk “at” Willamette University at 7:10pm EST that day; it’s online and you can come to the talk if you want to (or not, I’m not keeping track. It’s about Coding and Generative Design for 3D Printing.
- If you need help now or at any point: For math questions, use Canvas Chat or Discussion, or contact the SMLC. For other questions text Dr. Taalman directly.
Step 5: Take the Mastery Quiz for Section 7.5
- When you’re ready, take the 7.5 Mastery Quiz in Canvas (and retake if needed)
- I recommend you take your first quiz attempt by Friday or Saturday
- Click here to read details about quizzes - read BEFORE ATTEMPTING any quiz
You must finish the WebAssign homework and both quiz attempts before 11:59 pm on Sunday — but having said that, these are not normal times; please just text me if you need an extension due to personal, economic, or family situations.
Let me know how things are going by filling out this End-of-week-5 Survey.
Have a good week everyone! Please don’t hesitate to contact me if you need anything.